Oh, that is a shame ~ I don't have enough place names for realistic experiments.
I had assumed it would work like Google Maps that definitely gives a full 2,500 daily free quota every day.
However, nowadays Google Maps is a hassle to create an account and divulge a credit card that never gets charged if you restrict it to the free quotas, just to speed up the geocoding and get slightly better accuracy.

Mike - this time I remembered to select records before starting the geocoding to find out if that process would yield more coded locations in a single run.

I selected about 500 uncoded place records ie about twice the number which was getting coded in a "normal" session. The geocoding started at the lowest numbered selected place, and stopped after about 60 seconds. Before the process stopped, I can see that it had coded about 290 records. In other words, within the range I had been finding without selecting a group of records.

From now on, I will simply do a "map all places" run once a day, and should eventually have all locations coded.